New energy equality criteria of weak solutions of the incompressible magnetohydrodynamic equations

Abstract

In this paper, we are concerned with the validity of energy equality for weak solutions of the incompressible magnetohydrodynamic equations in the framework of anisotropic regularities. We present some new energy equality criteria which allow the velocity field to lie within the classical Shinbrot or Taniuchi-Beirão da Veiga-Yang energy equality classes, while permitting the magnetic field to extend beyond these classes. Furthermore, we also establish energy equality criteria in terms of the gradient of the velocity only.